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Explore the intriguing effects of electron wave functions in optoelectronics and transport in this comprehensive lecture. Delve into the fascinating world of Berry curvature and its role in creating anomalous electron velocity. Examine the formation of topological boundary states in bilayer graphene due to spatial gap inversion, and investigate the collective motion of these states through plasmons. Discover non-trivial optical responses in anomalous Hall materials, including cyclotron motion without magnetic fields and dynamical Hall currents that preserve time reversal symmetry. Conclude by exploring the impact of wave functions on electron hydrodynamics. This in-depth presentation offers valuable insights into advanced concepts in solid-state physics and their applications in modern electronic and optical devices.